It's pretty trivial for a company to make a mold for a plastic cartridge. The chips are nothing special, they are just ROMs. Cheap and widely available.
In fact, I'm pretty confident that a competent DIYer could 3D print a cartridge shell, flash a ROM, and etch a PCB in an afternoon or two.
For the Atari 2600, Game Boy, etc., the first cartridges were nothing more than a ROM chip on a printed circuit board. Later games sometimes included a lot more functionality on the cartridge (battery-backed save RAM, bank switching hardware, etc.) which does make things complicated very quickly. Today, programmable logic is sometimes used to replace old custom IC designs used in cartridges, or to design something new.
For games more complicated than a simple ROM chip, the Game Boy presents an interesting challenge: the cartridge is both very small and it needs to be able to run off battery power. That excludes using both a high-power-consumption modern SoC or FPGA, or using lots of discrete logic.
But if it'll fit in 32 KB, it's 3D print a case, order a PCB, and program a standard Flash chip.
> For the Atari 2600, Game Boy, etc., the first cartridges were nothing more than a ROM chip on a printed circuit board.
We've actually come full circle on this one. If you ever disassemble a Nintendo Switch Game Card that has a black area above the metal contacts, it doesn't even have a PCB. It's just a ROM chip, with metal contacts on the bottom shaped differently than your standard BGA pattern, contained in plastic. If it has a green area above the metal contacts, it's a PCB with the chip on the other side.
